If you are a current certified flight instructor (CFI), you may train sport pilot candidates, within the category/class listed on the on your CFI certificate. Obviously, you will need to become familiar with the sport pilot rules under 61 subpart J. The SPORT PILOT & CFI APPLICANT CHECKRIDE book will fill you in on everything you need to know.
If you are a current airplane CFI under subpart H and you want to instruct in a trike weight-shift control (WSC) light-sport aircraft (LSA), the first step is to recieve a proficiency check to add the WSC Sport Pilot rating. Once you obtain the pilot rating then you can add the instructor privileges.
Note that both the sport pilot weight-shift control trike pilot and weight-shift control trike CFI is a privilege and not an additional rating; as such you will not have to pass a checkride with an examiner but a proficiency check with a weight-shift control trike CFI as described below. It is possible to add a Private pilot WSC rating but this requires 40 hours WSC total (just like airplane) additional time. See Private Pilot WSC for details for obtaining this additional WSC Private Pilot rating.
If you are a current airplane CFI who wishes to instruct in trikes yet is not currently rated in WSC trikes, you must add the privilege at the sport pilot instructor level by proficiency check in accordance with FAR 61.419 as described below.
(a) Receive a logbook endorsement from the recommending authorized WSC trike instructor (CFIS #1) who trained you on the applicable areas of operation certifying you have met the aeronautical knowledge and flight proficiency requirements for the WSC trike category and class flight instructor privilege you seek;
(b) Complete an application for those privileges and obtain a recomendation for the instructor who trained you (CFIS#1) on a form and in a manner acceptable to the FAA (8710-11 form) and present this application to a seperate authorized WSC trike instructor (CFIS#2) to conduct the proficiency check;
(b) Successfully complete a proficiency check from the seperate authorized instructor (CFIS#2) other than the recommendating instructor who trained you for the WSC Trike category and class flight instructor privilege you seek;
(d) Receive a logbook endorsement from the instructor who conducted the proficiency check certifying you are proficient in the areas of operation and authorized for the WSC Trike category and class flight instructor privilege.
(e) Submit the 8710-11 form to the FAA to complete the process and become registered as a weight-shift control Trike instructor.